Thread: Critical numbers problem

Find all the critical numbers of the function f(x) = x+ln(|cos(x)|) that lie in the interval [pi, 3pi].

Please help, thanks in advance.

Hello, nubshat!

Exactly where is your difficulty?

Differentiate and equate to zero: .

We have: .

Hence: .

Answers: .

Doesn't the derivative fail to exist at and , so that they are critical points, too?

- Hollywood

would you also have to include the two end points at pi and 3pi?

Yes, I think both end points, too. Critical points are only used for finding minima and maxima, so assuming you're finding the minimum or maximum over the range to , then you would need to include those points, too.

I suppose it could be that you're finding the minimum or maximum over a different range, and for some reason you're temporarily limiting yourself to finding critical points in the given range. That doesn't make much sense, though.

- Hollywood